Interest in quantum information processing has grown dramatically in recent years because of recent successes in developing quantum systems and the expected capabilities of the technology. In particular, working quantum cryptosystems have been developed, and if large (many qubit) quantum computers can be built, quantum computers will perform many tasks much more efficiently than can classical computers. Quantum processors having tens or hundreds of qubits, for example, would be able to perform quantum simulations unreachable with any classical machine. Such quantum processors also have the potential to extend the working distances and applicability of quantum communications.
Many candidate technologies for quantum computing hardware are currently being studied. Whichever technology turns out to be most practical, quantum coherent communications will likely be needed for linking separate quantum processors. Coherent electromagnetic fields (as photonic qubits) seem ideal for communications between quantum computers and for general quantum communications because light, traveling either down optical fibers or even through free space, can carry quantum information over large distances. Further, some quantum computing may be performed directly on photonic qubits, using non-linear or linear quantum optical processes.
The interactions of photons with matter is likely to be an important ingredient in large-scale implementation of quantum information technology, and the ability to easily interconvert traveling photonic qubits and stationary matter qubits will be needed. Further, the ability to perform quantum gates (e.g., one-qubit and two-qubit gates) directly on qubits encoded into photon states is highly desirable for some quantum communications and computing.
FIG. 1 shows an exemplary system 100 in which photons interact with matter. In this example, system 100 includes an atom 110 and a low-loss resonator 120 that directs a unidirectional traveling electromagnetic wave of angular frequency ωa for interaction with atom 110. Atom 110 can actually be an ensemble of one or more atoms, molecules, or other systems having at least two accessible quantum energy levels. Two of the accessible energy states |1> and |2> of atom 110 differ in energy by an amount ω12, where is the reduced Planck constant. The energy (•ωa) of each photon in the traveling wave may be detuned from the energy difference between two energy levels of atom 110 as indicated in Equation 1, in which a detuning parameter νa is small relative to angular frequency ωa.•ωa=•(ω12+νa)  Equation 1
If atom 110 only has two accessible energy levels, atom 110 will have peak absorption of photons of energy •ωa when the detuning parameter νa is zero (i.e., when the photons are at a resonant frequency of atom 110). The absorption coefficient generally remains non-zero for other values of parameter νa.
Electromagnetically Induced Transparency (EIT) is a phenomenon that can make atom 110 transparent to the photons at frequency ωa in resonator 120. For EIT, atom 110 has at least three accessible energy levels, and a laser or other device applies an electromagnetic field referred to as a control field to atom 110 that creates quantum interference between the photonic and matter states.
FIG. 2A is a semi-classical energy level diagram comparing the energy levels of the three accessible energy states |1>, |2>, and |3> of atom 110 to the energy •ωa of a photon in resonator 120 and the energy •ωb of a photon in the control field applied to atom 110. As indicated in Equation 2, the energy •ωb of each photon in the control field is nearly equal to the energy difference ω32 between energy states |3> and |2> of atom 110 where a detuning parameter νb is small relative to angular frequency ωb.•ωb=•(ω32+νb)  Equation 2
FIG. 2B illustrates the energy levels of product states |X, A, B> of system 100. For product states |X, A, B>, X is 1, 2, or 3 indicating the energy level of atom 110, and A and B are the numbers of photons of angular frequencies ωa and ωb, respectively. Rabi frequencies Ωa and Ωb in FIG. 2B represent the rate of absorption and stimulated emission of photons of angular frequencies ωa and ωb caused by the electric dipole interaction of the electric field of the photons with the corresponding dipole moment of atom 110. An example of an absorption or stimulated emission of a photon in resonator 120 in system 100 is a transition between product states |1, na+1, nb> and |2, na, nb>. In a spontaneous emission, an excited atom 110 can scatter a photon into free space (e.g., in the transition from state |2, na, nb> to state |1, na, nb>).
The control field frequency ωb can be tuned to create quantum interference of the states of the photons and atom that minimize the rate at which atom 110 absorbs photons of angular frequency ωa. In particular, the absorption coefficient α(ωa) for atom 110 to absorb a photon of angular frequency ωa falls to zero when detuning parameter νa is equal to zero. The applied control field thus makes atom 110 transparent to photons in resonator 120.
For quantum information processing purposes, one useful interaction of atom 110 with a photonic signal would introduce a phase change in the expectation value of the electric field operator of the photons when atom 110 is transparent to the photons or otherwise cause no (or minimal) signal loss. However, when the absorption coefficient is zero (or minimal), a three-level atom 110 causes no (or minimal) phase change in the state of the transmitted photons. A three-level atom is thus not currently considered to be suited for introducing a phase change in a photonic qubit.
In view of the current state of the art, there is a need for identifying a system that allows for the interaction of photon quantum states or qubits with matter systems to introduce phase changes in the photon quantum states without otherwise absorbing or dephasing the photon states.